Dot Sensitivity Analysis of the Current Region for Topology Optimization in Magnetostatic Systems

This paper proposes dot sensitivity analysis of a current region for topology optimization. A continuum shape sensitivity formula is employed to derive a dot sensitivity formula in a simple closed form. The derived dot sensitivity formula provides the information on where the current dots should be created for topology optimization. This is necessary to generate the current dots in a vacant region of the design domain. Because this dot sensitivity analysis can obtain various topologies of material distribution, the possibility of local optimum convergence is reduced. Furthermore, because this dot sensitivity analysis does not require a specific initial design, its numerical implementation is simple. This dot sensitivity method is combined with the level set method to perform topology optimization. To demonstrate the usefulness of the proposed method, it is applied to two optimization problems of magnetic resonance imaging.